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Contract No. DE-AC36-08GO28308

Wind Power Plant Voltage 

Stability Evaluation

Preprint

E. Muljadi and Y. C. Zhang

National Renewable Energy Laboratory 

To be presented at the International Conference on Wind Energy

Grid-Adaptive Technologies

Jeju, Korea

October 20–22, 2014

Conference Paper

NREL/CP-5D00-62568

September 2014 
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Wind Power Plant Voltage Stability Evaluation

Eduard Muljadi* and Yingchen Zhang*

Abstract – Voltage stability refers to the ability of a power system to maintain steady voltages at all 

buses in the system after being subjected to a disturbance during a given initial operating condition. 

Voltage stability depends on a power system’s ability to maintain and/or restore equilibrium between load 

demand and supply. Instability that may result occurs in the form of a progressive fall or rise of voltages 

of some buses. Possible outcomes of voltage instability are the loss of load in an area or tripped

transmission lines and other elements by their protective systems, which may lead to cascading outages. 

The loss of synchronism of some generators may result from these outages or from operating conditions 

that violate a synchronous generator’s field current limit, or in the case of variable speed wind turbine 

generators, the current limits of power switches. This paper investigates the impact of wind power plants 

on power system voltage stability through using synchrophasor measurements.

Keywords: Wind Power Plant, Voltage Stability, Phasor Measurement Unit

1. Introduction

The U.S. power industry is undertaking several 

initiatives that will improve the operations of the electric 

power grid. One of those is the implementation of widearea measurements using phasor measurement units (PMUs) 

to dynamically monitor the operations and status of the 

network and provide advanced situational awareness and 

stability assessment.

Wind power as an energy source is variable in nature. 

Similar to other large generating plants, outputs from wind 

power plants (WPPs) impact grid operations; conversely, 

grid disturbances affect the behavior of WPPs. The rapidly 

increasing penetration of wind power on the grid has 

resulted in more scrutiny of every aspect of WPP operations 

and the demand that large WPPs should behave similarly to 

conventional power plants under normal and contingency 

grid conditions. The low-voltage ride-through requirement 

for WPPs is one such example. Other proposed 

requirements include frequency response and simulated 

plant inertia.

To completely describe the system condition (state) of 

the electric power grid at any instant, it is necessary to 

know the voltage (V), current (I), and apparent power (S) 

of every point (node/bus) on the system. All three quantities 

in an alternating-current power system are complex 

numbers that can be represented by phasors with both a 

magnitude and a phase angle. Of the three phasor quantities, 

only two (any two) are needed to derive the third based on 

the equation S = VI* = P + jQ. Advanced computing power 

and the worldwide availability of global positioning system 

(GPS) time signals make it possible for a PMU to measure 

voltage and current at a precise time and output these 

quantities in phasor form. GPS time signals can be accurate 

within 1 microsecond (μs) anywhere the signal is available. 

GPS time signals enable the synchronization of 

measurements across the very large distances that power 

system interconnections span. This new technology not 

only produces very accurate phasor measurements, but it 

also enables synchronized measurements in the same 

instant [1-9]. 

2. WPP Voltage Stability Evaluation

Voltage stability refers to the ability of a power system to 

maintain steady voltages at all buses in a system after being 

subjected to a disturbance from a given initial operating 

condition. Voltage stability depends on a power system’s 

ability to maintain and/or restore equilibrium between load 

demand and supply. Instability that may result occurs in the 

form of a progressive fall or rise of voltages of some buses.

Possible outcomes of voltage instability are the loss of 

load in an area or tripped transmission lines and other 

elements by their protective systems, which may lead to 

cascading outages. A loss of synchronism of some 

generators may result from these outages or from operating 

conditions that violate a field current limit of synchronous 

generator; or in the case of variable speed wind turbine 

generator, the current limits of power switches. Voltage 

stability may vary during the event; it can be short term (< 

1 minute), or it may evolve during many hours [10–11].

* National Renewable Energy Laboratory, Golden, CO, USA

(Eduard.Muljadi@nrel.gov, Yingchen.Zhang@nrel.gov)
2

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2.1 Parallel Compensation

Reactive power losses in a transmission line can be 

supplied from Bus 1 or Bus 2, or they can be shared by 

both sides. Parallel compensation can be implemented on 

both sides. Reactive compensation can be implemented by 

controlling the generator itself, or it can be provided from 

external compensation, such as adjustable capacitor banks, 

synchronous condensers, and static power compensation 

(static VAR compensator, SVC, or static compensation, 

STATCOM).

Figure 1. Two-bus system with available reactive power 

resource

Two possible compensations are commonly implemented 

in a WPP: one is reactive compensation at the turbine level 

(mostly in Type 1 and Type 2 wind turbine generators); the 

other is at the plant level (usually at the low side of the 

substation transformer). Plant-level compensation is usually 

added when a WPP is connected to a weak grid. Type 3 and 

Type 4 wind turbines are equipped with power converters 

that can provide controllable reactive compensation.

Consider Figure 1 (c), which shows that the voltage at 

Bus 1 and Bus 2 is maintained constant, and there is equal 

magnitude at 1.05 p.u. The reactive power is supplied by 

both Bus 1 and Bus 2. The voltage is adjusted to be 

constant; thus, as the output power from Bus 1 fluctuates, 

the reactive power must also be adjusted to follow the 

output power generated by Bus 1.

In this case:

φ1 = φ2 = δ/2

Thus, the reactive power generated by Bus 1 must follow:

Q = V1 I sin (δ/2)

And the reactive power can be commanded to follow the 

rules:

Q = P tan (δ/2)

P = V2 sin δ /Xs

With an active adjustment of reactive power generated 

by reactive power compensation at Bus 1 and Bus 2, the 

voltage level can be kept constant at varying wind power 

output. Note that this control helps to keep the voltage 

adjusted, but the power angle δ is not affected for the same 

amount of power delivery. Figure 2 shows an example of 

controlling reactive power to maintain equal contribution of 

reactive power from both sides of the buses.

Figure 2. Voltage phasor diagram with equal 

contribution of reactive power from both sides

2.2 Series Compensation

Reactive power compensation can also be accomplished 

by using series compensation (see Figure 3). The advantage 

of this is that the voltage and current rating of the series 

compensation is relatively small considering that it is 

intended to compensate for the voltage drop of the line 

impedance. Series compensation is commonly used to 

compensate long transmission lines; however, care must be 

taken not to make it prone to cause subsynchronous 

resonance.

Figure 3. Single-line diagram of a series-compensated 

system and a diagram of its voltage phasor

A typical WPP representation is shown in Figure 4. Note 

that the equivalent generator, pad-mounted transformer, and 

collector system can be derived easily from the actual 

collector system schedule [12–15].

V1 I V2 jXs

V1

V2

I

jXs I (a) All reactive 

power is supplied by 

Bus 1

(b) All reactive 

power is supplied by 

Bus 2

V1

V2

I

jXs I

V1

V2

I jXs I (c) All reactive power is 

supplied equally by both 

Bus 1 and Bus 2

φ

φ1 δ φ2

φ

δ

δ

 

V1

V2

I jXs I

V1

V2

I jXs I

δ

(a) Low wind speeds

(b) High wind speeds

V1 V2

I jXs

jXc V1C

By adjusting XC = 0.5 Xs, it is possible 

to generate an improved power factor at 

Bus 1 and reduce the power angle δ

between Bus 1 and Bus 2 for the same 

power delivery.

 V1C

 V1

V2

I

jXC I

δ
3

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Figure 4. WPP represented by a single generator

2.3 PV and PQ Curves

In this section, we show how to perform power-voltage 

(PV) and voltage–reactive power (VQ) power system 

stability analysis on a WPP. We use a single-turbine 

representation of a WPP. The WPP uses 1.5-MW Type 3

(variable-speed doubly-fed induction generator) wind 

turbines operated in variable-speed mode with a constant 

power factor, PF = 1.0. The total output power of the WPP 

is rated at 204 MW. The WPP is connected to the rest of the 

power system via its point of interconnection. Two grid 

conditions are used in this study: the stiff-grid and weakgrid conditions. The stiff-grid condition is simulated by 

connecting both of the transmission lines between Bus 1 

and Bus 2. The weak-grid condition is simulated by 

disconnecting one of the parallel lines between Bus 1 and 

Bus 2. The transmission lines are overhead lines with a 

very small shunt capacitance.

The collector system is built with underground cables 

and some overhead lines. Because the size of the WPP area 

is very large, the effective impedance between the 

substation and a turbine is different for each turbine. 

2.3.1 PV Capability Curve

A PV capability curve is normally conducted to measure 

the proximity of the rated operating condition of a WPP to 

the voltage collapse. In a large power system network, the 

level of the output power of a group of generators in the 

area and zone of interest are usually varied, and the other 

group of generators is reduced by the same amount of 

power to develop net-zero additional output power. For a 

WPP, a PQ characteristic map of the WPP is generally used,

and the WPP is operated from a low-wind to higher-wind 

condition with a pair of P&Q from the PQ characteristic 

map. Most wind turbine generators (Type 1 and Type 2) are 

normally compensated to have a unity power factor 

operation by using a switched capacitor. Type 3 and Type 4 

wind turbine generators are built with the capability to vary 

reactive power and can be operated to control voltage, 

reactive power, or the power factor output via a power 

converter control. Additional information related to PV and 

VQ curves as discussed in this section and the next and can 

be found in the references [10–11].

Figure 5. Voltage at the generator during stiff-grid and 

weak-grid conditions

In this investigation, we operate a Type 3 wind turbine at 

a unity power factor, thus generating only real power at the

terminals. No other reactive power compensation is 

provided at the turbine level or at the WPP level. The PV 

curves shown in Figure 5 were derived by measuring the 

bus voltage at the generator as we varied the output power 

of the wind turbine. Figure 5 shows both the weak grid and 

stiff grid. The real power margin for the grid is measured 

from the rated power (P = 1.0 p.u.) to the knee point at 

which the voltage collapses. Usually the computation does 

not converge beyond the knee point. In the simple case we 

study, the real power margin for the stiff grid is Pmargin-STIFF 

= 1.4 p.u. (= 280 MW) at voltage V = 0.77 p.u. Similarly, 

the real power margin for the weak grid is Pmargin-WEAK = 1.1 

p.u. (= 220 MW) at voltage V = 0.82 p.u. The voltage 

characteristic indicates that for a stiff grid we can increase 

the level of generation to 125% of rated power while 

keeping the bus voltage above 0.9 p.u.; however, for a weak 

grid the level of generation can be adjusted up to 97% rated 

before the voltage drops below 0.9 p.u. 

Wind turbine generators are operated in unity power 

factor mode; thus, no reactive power is supplied by the 

generator to the grid to compensate for the reactive losses 

within the collector systems inside a WPP, in the 

transformers, and the transmission lines. As shown in 

Figure 6, the reactive power losses are supplied by the grid 

(Bus 1 as the infinite bus). In both cases, the reactive power 

is shown to exhibit a nonlinear (slightly quadratic) function 

of the WPP output power, which is expected. Note that the 

reactive power needed for an output of 1.0 p.u. real power 

is 38% rated power for a stiff grid and 56% for a weak grid.

Gen

100-MW Equivalent 

Wind Turbine Generator

Infinite Bus

Ideal 

Gen

230-kV Line 1

R1, X1, B1

230-kV Line 2

R2, X2, B2

34.5-kV Collector 

System Equivalent

Re, Xe, Be

0.6/34.4-kV Equivalent 

GSU Transformer

Rte, Xte

34.4/230-kV 

Station Transformer

Rt, Xt.

Station-Level Shunt 

Compensation Turbine-Level Shunt 

Compensation

1 2 3

4

5
4

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Figure 6. Reactive power comparison at the infinite bus 

during weak-grid conditions

The above exercise is conducted by setting the generator 

to produce a unity power factor output power. It will give 

different results if the WPP is operated at different modes 

(e.g., constant power factor, constant voltage, constant 

reactive power).

2.3.2 VQ Capability Curve

A VQ capability curve is normally investigated to 

determine the reactive power adequacy in a WPP. Reactive 

power capability is an important aspect of controlling the 

voltage and influencing the PV characteristic behavior. 

As mentioned previously, the WPP uses Type 3 wind 

turbine generators. All of the wind turbines are controlled 

to regulate Bus 3 (at the low side of the substation 

transformer). The setting point of the regulated voltage is 

varied from 0.6 p.u. to 1.0 p.u., and the reactive power is 

plotted against the regulated voltage. The grid voltage 

(infinite bus) is set to 1.05 p.u. all the time, and the 

generator real power output is set to 1.0 p.u.

Figure 7. VQ characteristics of a wind turbine generator 

during stiff-grid and weak-grid conditions

Figure 7 shows the VQ curve of the wind turbine 

generator for both stiff- and weak-grid conditions in the 

normal operating region (0.95 p.u. < V < 1.05 p.u.). We 

assume that the participation factor for the generator in this 

case is 100% for each wind turbine generator; therefore, the 

output reactive power contribution for each individual 

generator is equal to each other.

The reactive power margins, at the minimum points of 

the curves, are shown by the different colors in Figure 7. 

The reactive margin for the stiff grid is Qmargin-STIFF = 0.32 

p.u. (= 64 MVAR) at V = 0.69 p.u. Similarly, the reactive 

margin for the weak grid is Qmargin-WEAK = 0.113 p.u. (= 22 

MVAR) at V = 0.75 p.u. This simple margin measurement 

is intended as an illustration only. For a larger network, the 

area and zone considered with many generators and loads 

need to be included.

2.4 PMU-Enhanced Dynamic Stability Assessment

PV and VQ capability curves are used without the need 

to know the phase angle of the phasor voltage. However, 

with the recent large-scale synchrophasor deployment, the 

availability of the phase angles can be used to enhance the 

prediction of voltage instability in a power system network.

To conduct a simple analysis performance in Positive 

Sequence Load Flow (PSLFTM) computer program, we use 

the same network shown in Figure 4. We observe three 

conditions:

1. A stiff power system network in which both parallel 

lines connecting the infinite bus and substation 

transformer are online

2. A stiff power system network with a reduction of 

infinite-bus voltage by 4%

3. The same initial condition as (1), but representing a 

weak power system by removing one line of the 

parallel lines connecting the infinite bus and the 

substation transformer

Then, at constant reactive output power, we increase the 

generation from 50% to above 100%, until the load flow 

does not converge, indicating the voltage collapse when the 

system reaches its instability limit. The operation is 

repeated at different values of reactive power. As expected, 

the power system reaches its instability operation at 

different output power levels depending on the size of 

reactive power.

2.4.1 Impact on the Voltage Magnitude

As we vary both the real and reactive power output of the 

WPP, the voltage magnitude and the phase angle at the 

generator change as the level of real power generation and 

the reactive power generation varies. Because the voltage is 

usually maintained within a tight range (0.95 p.u. < V < 

1.05 p.u.), whereas the phase angle has a wider range, it is 

common practice to keep the voltage as steady as possible. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.5 0.7 0.9 1.1 1.3 1.5

Reactive Power (p.u.)

Real Power (p.u.)

Q @Bus 1 Stiff-Grid

Q @ Bus 1 Weak-Grid
5

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Figure 8. Voltage characteristics of a wind turbine 

generator during stiff-grid conditions

As shown in Figure 8 through Figure 10, the reactive 

power output has a major impact on the generator voltage 

compared to the impact from the real power output.

Figure 8 illustrates an operation of a WPP connected to a 

stiff grid. First, consider that the WPP is operated at 1.0 p.u. 

output real power and the reactive power is set from Q = -

0.3 p.u. (generator-absorbing reactive power), which is 

increased to Q = 0.5 p.u. As shown on the contour map, the 

operating point moves along the vertical black line, and the 

generator voltage increases with additional reactive power 

supplied to the grid from Vt = 0.75 p.u. to 1.14 p.u. when 

the reactive power output is close to 1.14 p.u. This method 

of operation is also represented by the black line in Figure 7, 

which shows the VQ characteristic of the wind turbine 

generator operated with a stiff grid at rated power P = 1.0.

Similarly, when the generator is operated at unity power 

factor (Q = 0.0 p.u.) and the real power output is varied 

from 0.5 p.u. to 1.4 p.u., the operating point moves along 

the horizontal blue line. As shown, the generator voltage 

decreases from 1.01 p.u. to 0.75 p.u., at which point it is 

obvious that the voltage collapses (Vt = 0.75 p.u. at P = 

1.14 p.u.). This characteristic is illustrated in Figure 5 as 

the PV characteristic of the wind turbine generator operated 

with a stiff grid at unity power factor.

On the other hand, if the voltage is maintained at 1.0 p.u., 

the operating point follows the red line, the amount of 

reactive power varies from Q = -0.02 p.u. to Q = 0.5 p.u., 

and the voltage collapse does not yet occur. Note that at Q 

= 0.5 p.u., the output power that can be transferred through 

the transmission line is P = 1.75 p.u. (stable operation).

Figure 9. Voltage characteristics of a wind turbine 

generator during stiff-grid conditions with the infinite bus 

reduced by 4%

Figure 10. Voltage characteristics of a wind turbine 

generator during weak-grid conditions

Figure 9 represents a condition similar to that shown in 

Figure 8; however, the entire surface map shows a 

reduction in voltage. It is probably easier to view this in

three-dimension (3D) with the mountain shown in Figure 8

shrunk as the voltage at the reactive power of Q = 0.5 p.u. 

drops from 1.15 p.u. to 1.11 p.u. The voltage collapse area 

is shown to be slightly larger than it was in the previous 

one. Note that the shape of the curves remains very similar 

to those shown in Figure 8, but the new trajectory of Vt = 

1.0 p.u. (represented by the green curve) must be shifted 

upward in parallel to the old one (red curve) by 

approximately 4%.

Figure 10 also represents a condition similar to that 

shown in Figure 8; however, one of the parallel lines is 

tripped offline. This figure shows the higher slope of the 

voltage contour, larger area of the voltage collapse, and the 

equipotential line previously represented by the red line 

becomes the equipotential line represented by the blue line. 

Also shown is that the red line that was previously located 

0.5

0.3

0.1

0

- 0.1

- 0.3

REACTIVE POWER OUTPUT (P.U.)

0.5 0.72 0.94 1.16 1.38 1.6 1.82 2.04 

 

 REAL POWER OUTPUT (P.U.)
6

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in the stable region during a stiff-grid condition (Figure 8) 

is now part of the red line that enters the unstable (voltagecollapse) area, indicated by the area encircled by the dashed 

line.

2.4.2. Impact on the Voltage Angle 

As we vary both the real and reactive power output of the 

WPP, the voltage magnitude and the phase angle at the 

generator change as the level of real power generation and 

the reactive power generation varies. The contour map in

Figure 11 shows the phase-angle variation as the real and 

reactive power is varied during stiff-grid conditions. The 

rated output power P = 1.0 p.u. at voltage V = 1.0 p.u. 

requires a reactive power of 0.1 p.u. and voltage angle of 

δ = 23°. Compare this to the weak grid shown in Figure 12. 

In Figure 12, obtaining the voltage of V = 1.0 p.u. requires 

Q = 0.15 p.u. of reactive power and the voltage angle of 

30°. The line angle from Figure 11 was transferred to 

Figure 12 for reference. The δstiff = 23o becomes δweak = 31° 

with a lower slope. As shown in Figure 11 and Figure 12

for different grid strengths, the operating point in the PQ 

plane is represented by a pair of V, δ. Thus, by operating the 

generator in the normal operating voltage range, we can 

observe the value of the voltage angle; an increase δ angle 

after an event for the same power indicates a weaker grid 

condition.

0.5

0.3

0.1

0

- 0.1

- 0.3

0.5 0.72 0.94 1.16 1.38 1.6 1.82 2.04 

 

 REAL POWER OUTPUT (P.U.)

δ = 23ο

Vt = 1.0 p.u.

P = 1.0 p.u. 

Q = 0.1 p.u.

Figure 11. Angle characteristics of a wind turbine 

generator during stiff-grid conditions 

In addition, the increase of reactive power needed to 

maintain per-unit voltage will always be an indication of a 

weaker grid. Caution must be taken when considering the 

impact on the size of the voltage-collapse area. A weaker 

grid means a larger voltage collapse area. One way to 

gauge the operating condition is to run or record an 

operation in a normal condition as the baseline, find a set of 

weaker grid conditions to map the operating characteristics 

of the WPP under different grid conditions, and eventually 

use these maps to guide the operation of the WPP and the 

proximity to an instability condition.

Figure 12. Angle characteristics of a wind turbine 

generator during weak-grid conditions 

Figure 13. Voltage-angle characteristics for a stiff grid 

with a change in the voltage magnitude

Figure 13 illustrates the movement of the operating point 

when there is a voltage reduction downstream. Assume that 

the operating Point A of the WPP is at rated power (P = 1.0 

p.u., V = 1.0 p.u., Q = 0.1 p.u.) on a stiff grid with the star 

symbol (δ = 23°). If there is a voltage reduction at the 

infinite bus by 4% without any changes in the line 

impedance, without changing the reactive power output of 

the generator the operating point moves to Point B (the 

voltage is reduced to 0.96 p.u. and the phase angle is 

increased δ = 25°). To maintain the voltage at V = 1.0 p.u., 

the reactive power must be increased by 0.1 p.u. (Point B’), 

with the phase angle (δ = 24°) slightly higher than the 

original Point A. Figure 14 shows the significant change in 

angle δ because of the exposure to a weaker grid. Assume 

that instead of a voltage reduction at the infinite bus, a 

parallel line is disconnected and we are exposed to a weak 

grid. The operating point of the WPP at rated power (P = 

1.0 p.u.) moves from Point A (V = 1.0 p.u.; δ = 23°) to 

Point C (V = 0.97 p.u.; δ ~ 30°). There is a significant 

0 10 20 30 40 50 0.4

0.6

0.8

1

P = 0.5 p.u.

P = 0.75 p.u.

P = 1.0 p.u.

P = 1.2 p.u.

P = 1.4 p.u.

Stiff Grid

Delta Angle (degrees)

Voltage Magnitude (p.u.)

 

 

 

 

0 10 20 30 40 50 0.4

0.6

0.8

1

P = 0.5 p.u.

P = 0.75 p.u.

P = 1.0 p.u.

P = 1.2 p.u.

P = 1.4 p.u.

Stiff Grid - with reduced voltage (4%)

Delta Angle (degrees)

Voltage Magnitude (p.u.)
7

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change in the phase angle ∆δ = 7° from A to C. Increasing 

the reactive power Q by 0.05 p.u. will return the voltage 

back to 1.0 p.u. and initiate a small reduction of the phase 

angle δ = 28°).

Figure 14. Voltage-angle characteristic for a weak grid

With this understanding, we can trace the operating point 

and understand the changes that occur in the power system 

network.

3. Summary

In modern WPPs, wind turbine generators are equipped 

with power converters to allow variable-speed operation. 

The use of power converters basically isolates the 

mechanical response from the grid, thus allowing more 

flexible operations of WPPs compared to conventional 

plants.

Voltage stability refers to the ability of a power system to 

maintain steady voltages at all buses in a system after being 

subjected to a disturbance relative to a given initial 

operating condition. It depends on the ability to maintain 

and/or restore equilibrium between load demand and load 

supply from the power system. Instability that may result 

occurs in the form of a progressive fall or rise of voltages 

of some buses.

In a conventional power plant, the balance of reactive 

power is shared among the generator, line impedance, and 

reactive component of the load. Very often, the imbalance 

is caused by sudden changes in the loads (in/out), and the 

limitation of the tap changer steps in a transformer or the 

limitation of the generator to provide additional reactive 

power when the upper limit of the exciter or the limitation 

of switched bank capacitors has been reached to provide a 

fine adjustment to match the required reactive 

compensation. 

The same limitation is also applicable to WPPs, because 

there is a current-carrying limit of the ability of the power 

electronic switches to carry the instantaneous reactive 

current demand needed. Another factor in WPPs is that the

size of a WPP can be very large, as such that the farthest 

wind turbine generator from the substation cannot provide 

reactive power as effective as the turbine closest to the 

substation. This is because, to provide reactive power, the 

sending end will have higher voltage, and if the line 

impedance between the turbine and the substation 

transformer is too large, the voltage limit of the power 

converter is sometimes reached before the amount of 

reactive power demand can be supplied.

Acknowledgement 

This work was supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

the National Renewable Energy Laboratory.

References 

[1] Kundur, P.; Paserba, J.; Ajjarapu, V.; Andersson, 

G.; Bose, A.; Canizares, C.; Hatziargyriou, N.; Hill, 

D.; Stankovic, A.; Taylor, C.; Van Cutsem, T.; 

Vittal, V. “Definition and Classification of Power 

System Stability.” IEEE/CIGRE Joint Task Force 

on Stability Terms and Definition, IEEE 

Transactions on Power Systems (19:2), May 2004.

[2] Stevenson, W.D. Elements of Power Systems 

Analysis, Fourth Edition. New York: McGraw Hill, 

1982.

[3] Grainger, J.; Stevenson, Jr., W. Power System 

Analysis. ISBN-10: 0070612935, ISBN-13: 978-

0070612938. New York: McGraw Hill, 1994. 

[4] Muljadi, E.; Mills, Z.; Foster, R.; Ellis, A.; Conto, J. 

“Fault Analysis at a Wind Power Plant for One Year 

of Observation.” Preprint. Prepared for the 2008 

IEEE Power and Energy Society General Meeting, 

July 20–24, 2008, Pittsburgh, Pennsylvania.

[5] Miller, N.W.; Sanchez-Gasca, J.J.; Price, W.W.; 

Delmerico, R.W. “Dynamic Modeling of GE 1.5-

and 3.6-MW Wind Turbine Generators for Stability 

Simulations.” IEEE Power Engineering Society 

General Meeting Proceedings; Jun. 2003, pp. 1977–

1983.

[6] Ellis, A.; Muljadi, E.; Sanchez-Gasca, J.; 

Kazachkov, Y. “Generic Models for Simulation of 

Wind Power Plants in Bulk System Planning 

Studies.” Preprint. Prepared for the IEEE Power and 

Energy Society General Meeting, July 24–29, 2011, 

San Diego, California.

[7] Muljadi, E.; Nguyen, T.B.; Pai, M.A. “Impact of 

Wind Power Plants on Voltage and Transient 

Stability of Power Systems.” Preprint. Presented at 

the IEEE Energy 2030 Conference, Nov. 17–18, 

2008, Atlanta, Georgia. 

[8] Federal Energy Regulatory Commission. Order 661. 

Appendix G: Large Generator Interconnection 

Agreement, LVRT requirement.

0 10 20 30 40 50 0.4

0.6

0.8

1

P = 0.5 p.u.

P = 0.75 p.u.

P = 1.0 p.u.

P = 1.2 p.u.

P = 1.4 p.u.

Weak Grid

Delta Angle (degrees)

Voltage Magnitude (p.u.)
8

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

[9] Muljadi, E.; Butterfield, C.P.; Parsons, B.; Ellis, A. 

“Effect of Variable-Speed Wind Turbine Generator 

on Stability of a Weak Grid.” IEEE Transactions on 

Energy Conversion (22), 2007; pp. 29–36. 

[10] WECC Undervoltage Load Shedding Task Force, 

Technical Studies Subcommittee. Under-Voltage 

Load Shedding Guidelines. July 1999. 

[11] WECC Reactive Power Reserve Work Group, 

Technical Studies Subcommittee. Voltage Stability 

Criteria, Under-Voltage Load Shedding Strategy, 

and Reactive Power Reserve Monitoring 

Methodology. May 2008.

[12] WECC Wind Generator Modeling Group. WECC 

Wind Power Plant Power Flow Modeling Guide.

May 2008. 

[13] WECC Modeling and Validation Work Group, 

Renewable Energy Modeling Task Force. WECC 

Wind Power Plant Dynamic Modeling Guide. 

January 2011. 

[14] Brochu, J.; Larose, C.; Gagnon, R. “Generic 

Equivalent Collector System Parameters for Large 

Wind Power Plants.” IEEE Transactions on Energy 

Conversion (26:2), June 2011.

[15] Brochu, J.; Larose, C.; Gagnon, R. “Validation of 

Single- and Multiple-Machine Equivalents for 

Modeling Wind Power Plants.” IEEE Transactions 

on Energy Conversion (26:2), June 2011.

Eduard Muljadi received his Ph.D. in electrical 

engineering from the University of Wisconsin at Madison. 

From 1988 to 1992, he taught at California State University,

at Fresno. In June 1992, he joined the National Renewable 

Energy Laboratory, in Golden, Colorado. His current 

research interests are in the fields of electric machines, 

power electronics, and power systems in general, with an 

emphasis on renewable energy applications. He is member 

of Eta Kappa Nu and Sigma Xi, a fellow of the Institute of 

Electrical and Electronics Engineers (IEEE), and an editor 

of the IEEE Transactions on Energy Conversion. He is 

involved in the activities of the IEEE Industry Application 

Society (IAS), Power Electronics Society, and Power and 

Energy Society (PES). He is currently a member of various 

committees of the IAS, and a member of the Working 

Group on Renewable Technologies and the Task Force on 

Dynamic Performance of Wind Power Generation, both of 

the PES. He holds two patents in power conversion for 

renewable energy.

Yingchen (Y.C.) Zhang received his B.S. from Tianjin 

University, in Tianjin, China, in 2003, and his Ph.D. degree 

from Virginia Polytechnic Institute and State University, in 

Blacksburg, in 2010. He is currently with the National 

Renewable Energy Laboratory. His research interests 

include power system stability with large-scale integration 

of renewable energies, power system wide-area monitoring, 

and PMU applications for renewable integrations. Zhang 

previously worked for the California Independent System 

Operator developing and implementing steady-state and 

dynamic analysis tools to improve power system situational 

awareness. He has been a member of IEEE since 2007.